Two points:

1) Hawaiian Airlines has a HNL hub that is quickly expanding, and DL serves the trans-pacific market to Asia well, in addition to JAL. HNL is so far from LHR, why would BA want to have anything to do with this mostly leisure market? It is well served by the OW alliance (AA + JL + QF).

2) If you are suggesting that BA operate flights from Hawai'i to the US mainland, this is only possible as a add-on flight into and out of the US. Because of cabotage (the prohibition of foreign airlines from operating internal US flights), BA could do something a la QF's flight from JFK to LAX, but it would not be able to pick up passengers originating in LAX, for example, and take them to HNL.

I would love it as much as the next person if BA could operate within the US. It would be a huge, huge improvement especially on transcontinental and flights to Hawai'i. But until the ridiculous rules regarding cabotage are lifted, it just isn't going to happen. The closest thing we have to a European airline operating in the US is Virgin America, and they got the third degree when trying to start-up because of their ties to Richard Branson and the global Virgin brand name.